On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line
From MaRDI portal
Publication:481981
DOI10.1016/j.jmaa.2014.10.077zbMath1309.34039arXiv1409.4602OpenAlexW2951830236MaRDI QIDQ481981
Rodrigo D. Euzébio, Jaume Llibre
Publication date: 19 December 2014
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.4602
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Discontinuous ordinary differential equations (34A36)
Related Items (47)
Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones ⋮ Bifurcation of limit cycles for a perturbed piecewise quadratic differential systems ⋮ On Hilbert’s 16th Problem for Some Discontinuous Piecewise Differential Systems ⋮ Existence of four-crossing-points limit cycles in planar sector-wise linear systems with saddle-saddle dynamics ⋮ Maximum number of limit cycles for certain piecewise linear dynamical systems ⋮ Bifurcation of the critical crossing cycle in a planar piecewise smooth system with two zones ⋮ Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center ⋮ Limit cycles of generic piecewise center-type vector fields in \(\mathbb{R}^3\) separated by either one plane or by two parallel planes ⋮ Piecewise linear differential systems without equilibria produce limit cycles? ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Limit cycles in planar piecewise linear differential systems with nonregular separation line ⋮ The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems ⋮ The 16th Hilbert problem for discontinuous piecewise linear differential systems separated by the algebraic curve \(y = x^n\) ⋮ Limit Cycles for a Class of Piecewise Smooth Quadratic Differential Systems with Multiple Parameters ⋮ Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop ⋮ The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems ⋮ The limit cycles of a class of piecewise differential systems ⋮ The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems ⋮ Uncountably many cases of Filippov's sewed focus ⋮ The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves. II ⋮ Heteroclinic loop bifurcations by perturbing a class of \(\mathrm{Z}_2\)-equivariant quadratic switching Hamiltonian systems with nilpotent singular points ⋮ Realization of Arbitrary Configuration of Limit Cycles of Piecewise Linear Systems ⋮ Periodic orbits in piecewise Riccati vector fields ⋮ Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Limit Cycles for Discontinuous Planar Piecewise Linear Differential Systems Separated by an Algebraic Curve ⋮ Limit cycles in the discontinuous planar piecewise linear systems with three zones ⋮ Limit cycles for a discontinuous quintic polynomial differential system ⋮ Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ The number and stability of limit cycles for planar piecewise linear systems of node-saddle type ⋮ Hopf-like bifurcations and asymptotic stability in a class of 3D piecewise linear systems with applications ⋮ On the study and application of limit cycles of a kind of piecewise smooth equation ⋮ Limit Cycles Induced by Threshold Nonlinearity in Planar Piecewise Linear Systems of Node-Focus or Node-Center Type ⋮ Poincaré Maps of “ <”-Shape Planar Piecewise Linear Dynamical Systems with a Saddle ⋮ Limit Cycles in a Family of Planar Piecewise Linear Differential Systems with a Nonregular Separation Line ⋮ Explicit non algebraic limit cycle for a discontinuous piecewise differential systems separated by one straight line and formed by linear center and linear system without equilibria ⋮ The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line ⋮ The Number of Limit Cycles Bifurcating from a Degenerate Center of Piecewise Smooth Differential Systems ⋮ Limit Cycles in Discontinuous Planar Piecewise Linear Systems Separated by a Nonregular Line of Center–Center Type ⋮ LIMIT CYCLE BIFURCATIONS IN DISCONTINUOUS PLANAR SYSTEMS WITH MULTIPLE LINES ⋮ LIMIT CYCLES OF PIECEWISE LINEAR DYNAMICAL SYSTEMS WITH THREE ZONES AND LATERAL SYSTEMS ⋮ Existence of Invariant Cones in General 3-Dim Homogeneous Piecewise Linear Differential Systems with Two Zones ⋮ Crossing limit cycles for discontinuous piecewise differential systems formed by linear Hamiltonian saddles or linear centers separated by a conic ⋮ On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Piecewise linear perturbations of a linear center
- On the number of limit cycles in general planar piecewise linear systems
- On Hopf bifurcation in non-smooth planar systems
- The qualitative analysis of a class of planar Filippov systems
- On the number of limit cycles in general planar piecewise linear systems of node-node types
- Piecewise linear differential systems with two real saddles
- Existence of limit cycles in general planar piecewise linear systems of saddle-saddle dynamics
- A general mechanism to generate three limit cycles in planar Filippov systems with two zones
- Piecewise-smooth dynamical systems. Theory and applications
- Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane
- On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
- Planar systems of piecewise linear differential equations with a line of discontinuity
- LOWER BOUNDS FOR THE MAXIMUM NUMBER OF LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A STRAIGHT LINE OF SEPARATION
- Resonance near border-collision bifurcations in piecewise-smooth, continuous maps
- Global properties of continuous piecewise linear vector fields. Part I: Simplest case in ℝ2
- Centennial History of Hilbert's 16th Problem
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones
- Canonical Discontinuous Planar Piecewise Linear Systems
This page was built for publication: On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line
